using Upset for defining positive real values (Re: Can I get ComplexExpand to really work?)

To: mathgroup at smc.vnet.net

Subject: [mg14670] using Upset for defining positive real values (Re: Can I get ComplexExpand to really work?)

From: Maarten.vanderBurgt at icos.be

Date: Sat, 7 Nov 1998 02:10:27 -0500

Sender: owner-wri-mathgroup at wolfram.com

Hello,
In functions like Solve and Simplify there is no option like the
Assumptions option in Integrate.
In a recent message ([mg14634]) Kevin McCann(?) suggested usign Upset as
an alternative to the Assumptions option in Integrate. I thought this
might work as well for Solve, Simplify etc.
In the example below I want A to be positive real number. I use Upset to
give A the right properties.
I was hoping Solve[A^2-1 == 0, A] would come up with the only possible
solution given that A is a positive real: {A -> 1}. Same for
Simplify[Sqrt[A^2]]: I would expect the result to be simply A (instead
of Sqrt[A^2]) when A is set to be positive and real.
Upset does not seem to work here.
1st question: why?
2nd question: is there a way you can introduce simple assumptions about
variables in order to rule out some solutions or to reduce the number
of solutions from functions like Solve, or to get a more simple answer
from manipulation fuctions like Simplify.
In[1]:= Sign[a]^=1;
Re[a]^=a;
Im[a]^=0;
In[2]:= ?a
"Global`a"
Im[a] ^= 0
Re[a] ^= a
Sign[a] ^= 1
In[3]:= Solve[a^2-1 == 0, a]
Out[4]= {{a -> -1},{a -> 1}}
In[5] := Simplify[Sqrt[a^2]]
Out[5]= Sqrt[a^2]
thanks for any help
Maarten van der Burgt
___________________________________________________________________________
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Maarten van der Burgt
R&D Department
ICOS Vision Systems
Esperantolaan 9
B-3001 Leuven
Belgium
tel. + 32 16 398220 direct + 32 16 398316 fax. + 32 16
400067
e-mail: maarten.vanderburgt at icos.be
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